Question: 6 people can paint 7 walls in 44 minutes. How many minutes will it take for 9 people to paint 9 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 6\text{ people}\\ t &= 44\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{44 \cdot 6} = \dfrac{7}{264}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 9 walls with 9 people. $t = \dfrac{w}{r \cdot p} = \dfrac{9}{\dfrac{7}{264} \cdot 9} = \dfrac{9}{\dfrac{21}{88}} = \dfrac{264}{7}\text{ minutes}$ $= 37 \dfrac{5}{7}\text{ minutes}$ Round to the nearest minute: $t = 38\text{ minutes}$